To get the numbers that Rachel can choose, we will need to list out the multiples of 5, 6, and 10 that fall between 49 and 95 and then pick the common numbers from them.
Multiples of 5:
[tex]50,55,60,65,70,75,80,85,90[/tex]Multiples of 6:
[tex]54,60,66,72,78,84,90[/tex]Multiples of 10:
[tex]50,60,70,80,90[/tex]Looking at the numbers above, the common multiples are:
[tex]60,90[/tex]